Group-III-element nitride semiconductors have been used in the field of heterojunction high-speed electron devices or photoelectron devices (semiconductor lasers, light emitting diodes, sensors, etc.), for example. Among the Group-III-element nitride semiconductors, gallium nitride (GaN) in particular has been gaining attention. Heretofore, gallium nitride single crystal has been obtained by reacting gallium with nitrogen gas directly (J. Phys. Chem. Solids, 1995, 56, 639). In this case, however, an extremely high temperature of 1300° C. to 1600° C. and an extremely high pressure of 8000 to 17000 atm (about 800 to about 1700 MPa) are required. In order to solve this problem, a technique for growing gallium nitride single crystal in a sodium (Na) flux (hereinafter such a technique also is referred to as a “Na flux method”) has been developed (e.g., U.S. Pat. No. 5,868,837). According to this method, it is possible to reduce the required heating temperature drastically to 600° C. to 800° C. and also the required pressure to about 50 atm (about 5 MPa). However, the single crystal obtained by this method is blackened, thereby posing a problem in quality. Furthermore, although the temperature and pressure required by this method are much lower than those required when producing the single crystal by reacting gallium with nitrogen gas directly, the conditions required by this method are still stringent, and there are demands for further reduction, especially in the required pressure. Moreover, conventional techniques cannot produce bulk-sized large transparent gallium nitride single crystal that has a low dislocation density and is of high quality. Besides, the conventional techniques can achieve only a poor yield. More specifically, according to the conventional techniques, the growth rate of the single crystal is extremely slow, for example, about a few micrometers per hour. Thus, even when gallium nitride is grown for 1000 hours, the size of the obtained single crystal is only about a few millimeters. In fact, the largest gallium nitride single crystal that has ever been reported had a maximum diameter of only about 1 cm. Thus, it has been difficult to put gallium nitride to practical use. A method for growing gallium nitride single crystal by reacting lithium nitride (Li3N) with gallium also has been reported (Journal of Crystal Growth 247 (2003) 275-278), for example. However, according to this method, the size of the obtained crystal is only about 1 to 4 mm. The above-described problems are not specific to gallium nitride, but may occur in other Group-III-element nitride semiconductors.